Suppose that we have the following joint distribution for random variables X and Y: XnY 0 1 0.08 0.12 0.2 0.30 2 0.12 0.18 a) Verify that this is indeed a probability distribution. b) What are the marginal distributions for X and Y? c) What are the means of X and Y? d) What is the conditional distribution of X given Y = 0? Also for X given Y = 1 : e) What do you notice about this result. Does this show that X and Y are independent? f) How does the conditional mean of X depend on Y? ) Does the result in (f) indicate if the random variables are independent? Be clear. h) What is the correlation between X and Y? (think before you work on this)